Annuities, often sold as "lifetime income plans" are products created and sold by insurance companies. I like to think of them as the opposite of life insurance. With life insurance, you are hedging the fact that you might die early. With an annuity, you are hedging the fact that you might live a really, really long time. Annuities are contracts that give you certain stated guarantees in return for certain payments.
If you are looking for a place to invest your money, look to stocks, bonds, mutual funds and other securities. If you are looking for guarantees and promises, look to insurance products.
Here's an article from Bloomberg Magazine that highlights some of the confusion with annuities.